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This paper presents an optimal construction of $N$-bit-delay almostinstantaneous fixed-to-variable-length (AIFV) codes, the general form of binarycodes we can make when finite bits of decoding delay are allowed. The presentedmethod enables us to optimize lossless codes among a broader class of codescompared to the conventional FV and AIFV codes. The paper first discusses theproblem of code construction, which contains some essential partial problems,and defines three classes of optimality to clarify how far we can solve theproblems. The properties of the optimal codes are analyzed theoretically,showing the sufficient conditions for achieving the optimum. Then, we proposean algorithm for constructing $N$-bit-delay AIFV codes for given stationarymemory-less sources. The optimality of the constructed codes is discussed boththeoretically and empirically. They showed shorter expected code lengths when$N\ge 3$ than the conventional AIFV-$m$ and extended Huffman codes. Moreover,in the random numbers simulation, they performed higher compression efficiencythan the 32-bit-precision range codes under reasonable conditions.

Optimal Construction of N-bit-delay Almost Instantaneous Fixed-to-Variable-Length Codes